Define Circle Knowing Two Points and ARC LENGTH Only.

Main Question or Discussion Point

I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!

I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!

There doesn't really need to be a context. You know the length of a chord on the circle and the length of the arc segment between them. I did some digging and did finally manage to find two solutions. One uses Newton's approximation method and the other uses and taylor expansion: